1. **State the problem:** Solve the equation $$x(y-z)p + y(z-x)q = \frac{x-y}{xy}$$ for variables $p$ and $q$. 2. **Understand the equation:** This is a linear equation in terms of $p$ and $q$ with coefficients depending on $x$, $y$, and $z$. 3. **Rewrite the equation:** $$x(y-z)p + y(z-x)q = \frac{x-y}{xy}$$ 4. **Isolate $p$ and $q$:** We can think of this as a linear equation: $$A p + B q = C$$ where $$A = x(y-z), \quad B = y(z-x), \quad C = \frac{x-y}{xy}$$ 5. **Note:** Since there is only one equation with two unknowns $p$ and $q$, the solution will be a parametric line or require additional constraints. 6. **Express $p$ in terms of $q$:** $$p = \frac{C - B q}{A} = \frac{\frac{x-y}{xy} - y(z-x) q}{x(y-z)}$$ 7. **Simplify numerator and denominator:** $$p = \frac{\frac{x-y}{xy} - y(z-x) q}{x(y-z)} = \frac{x-y}{x y \cdot x (y-z)} - \frac{y(z-x)}{x(y-z)} q = \frac{x-y}{x^2 y (y-z)} - \frac{y(z-x)}{x(y-z)} q$$ 8. **Final solution:** $$p = \frac{x-y}{x^2 y (y-z)} - \frac{y(z-x)}{x(y-z)} q$$ This expresses $p$ in terms of $q$ and parameters $x,y,z$. Without more equations, this is the general solution. **Answer:** $$p = \frac{x-y}{x^2 y (y-z)} - \frac{y(z-x)}{x(y-z)} q$$